The Gravity field and steady-state ocean circulation explorer (GOCE) satellite mission which measures the Earth's gravity field with an unprecedented accuracy at short spatial scales promises to significantly advance the research of geodetic ocean mean dynamic topography (MDT). To fully exploit the GOCE's advantages and precisely determine the MDT and its associated geostrophic currents globally and regionally, we must quantify the spatial resolution of GOCE-derived MDT and the geostrophic currents' retrieving ability of GOCE. Global MDT is firstly retrieved from the GOCE earth gravity field model (GO-CONS-GCF-2-TIM5) and the altimetry sea surface height model (CNES-CLS2011_MSS) by the spectral-wise approach which can effectively suppress the omission errors. Then the Gaussian filter method is used to suppress the noise of raw MDT results. To acquire the optimal spatial filter radius of the Gaussian filter, we calculate the RMS difference between the buoy-derived geostrophic currents and those calculated from the geodetic MDT with different filter radii. Those filter radii which make the above RMS difference acquired to be minimum are the best choice of the Gaussian filter radius. Based on this filter radius determining strategy, the optimal filter radii of MDT are determined in regional, zonal and global areas. The above optimal MDTs are then used to determine the corresponding geostrophic current fields. Finally, the characteristics of GOCE-derived geostrophic currents are studied carefully by three statistics factors, i.e. the RMS differences, correlation coefficients, and the speed proportion coefficients, between geodetic and buoy-derived geostrophic currents data. (1) The optimal spatial filter radii of GOCE MDT are 102 km, 131 km, 154 km and 127 km in the regions of south and north latitudes greater than 40°, between 20° and 40°, less than 20° and the global range, respectively, which are 24 km, 27 km, 21 km and 27 km better than that of GRACE. (2) The comparison between geostrophic currents acquired from MDT and buoy data shows that 1) in strong current regions, the speed (amplitude of velocity) of buoy derived geostrophic current can be explained 70% by geostrophic current acquired from MDT; and 2) the geostrophic current speeds derived from GOCE and altimeter data are closer to the buoy data compared with that of GRACE and altimeter data. (3) The correlation coefficients of geostrophic speed derived from two different geodetic MDTs (GOCE and GRACE) and buoy-derived current speed have obvious spatial characteristics. The correlation coefficients based on GOCE results are higher than that of GRACE in the Antarctic circumpolar current region, north Atlantic region and Agulhas region, but vice versa in the equator region. (4) The RMS differences of geostrophic current velocity calculated from GOCE MDT and buoy-derived current velocity are generally smaller than that of GRACE in strong geostrophic currents regions (except the equator region). For example, the above RMS differences in GOCE results are 16% and 24% smaller than that of GRACE results in the North Atlantic and Agulhas region, respectively. Firstly, the regional optimized filter radii of MDT are somewhat distinct in different regions. The filter radius is shorter in strong current regions than the low current speed regions at the same latitude, which decreases with the increasing latitude on average. Secondly, the GOCE geoid has good signal to noise ratio at short wavelength than that of GRACE geoid, which enables the use of shorter optimal filter radius of corresponding GOCE based MDT than that of the earlier GRACE based MDT. Furthermore, shorter optimal filter radius of GOCE based MDT ensures the GOCE based MDT and its associated geostrophic currents retain more information on small spatial scales. Lastly, the GOCE-based geostrophic currents are better than that of GRACE-based results in middle and high latitude regions.
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